In probability theory a sample space is a set containing all possible outcomes of an experiment and an event is a subset of the sample space (an element of its power set). I think it would be natural to think of the basis of the vector space representing a quantum system as a sample space and the quantum states of the system as events, right? But then it seems like an event shouldn't be simply a subset of the sample space.. Does that mean that the concept of a event can be further abstracted? How does quantum mechanics fit in with probability theory? Or does quantum mechanics use a different definition of probability? If guess my question is: is the probability used in quantum mechanics an abstraction or an instance of ordinary probability theory?